Voros product and noncommutative inspired black holes

Abstract

We emphasize the importance of the Voros product in defining noncommutative inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner-Nordström black holes show that the area law holds upto order $\frac{1}{\sqrt{\theta }}{e}^{-M^2/\theta }$. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy $E$ for these black holes is then obtained and a deviation from the standard identity $E=2S{T}_H$ is found at the order $\sqrt{\theta }{e}^{-M^2/\theta }$. This deviation leads to a nonvanishing Komar energy at the extremal point $T_H=0$ of these black holes. The Smarr formula is finally worked out for the noncommutative Schwarzschild black hole. Similar features also exist for a deSitter--Schwarzschild geometry.

To appear in Mod. Phys. Lett. A. This paper is an expanded version of earlier works. Some new results have also been added

References in corpus (1)

• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics

Cited by in corpus (1)

• Signatures of quantum geometry from exponential corrections to the black hole entropy